arXiv subjects

Zhen Dai

Publications and source records attributed to Zhen Dai.

12 recordsLinked to original sources

arXiv2026

Optimal sizing of a hydrogen-based direct reduced iron-electric arc furnace system integrated with methanol synthesis toward zero-carbon steel production

A hydrogen-based direct reduced iron-electric arc furnace system integrated with methanol synthesis (H2-DRI-EAF-MeOH) provides a feasible pathway toward zero-carbon steel production. However, the volatility and intermittency of renewable energy sources (RES) may lead to capacity oversizing, while conventional annualized-cost and levelized-cost metrics are insufficient to evaluate investment return. To address these issues, this paper develops a fractional programming-based optimal sizing model for the H2-DRI-EAF-MeOH system. Hourly production rate limits are decoupled from annual production capacities and formulated as independent decision variables. Theoretical analysis demonstrates that increasing hourly production rate limits expands the multi-period operating feasible region, increases the theoretical upper bound on RES matching, and provides an investment-efficiency condition for increasing production rate limits. The annualized net return on investment (ANROI) is then adopted to represent investment return, and the resulting mixed-integer linear fractional programming model is solved using the Dinkelbach method. Case studies show that compared with the annualized net return (ANR) benchmark, the ANROI-based sizing yields higher internal rates of return (IRR), reaching 20.67% and 17.08% under the on-grid and off-grid scenarios, respectively. As the equivalent annual operating hours decrease from 8000 to 4000 h, the IRR increases from 19.68% to 20.67% under the on-grid scenario and from 12.64% to 17.08% under the off-grid scenario, while the corresponding battery storage capacities decrease by 113.56 and 796.31 MWh. The off-grid zero-carbon constraint enables CO2-to-MeOH conversion but reduces the system IRR to 14.99%, indicating that the resulting revenues are insufficient to offset the additional costs.

eess.SY↗

arXiv2025

ACD-CLIP: Decoupling Representation and Dynamic Fusion for Zero-Shot Anomaly Detection

Pre-trained Vision-Language Models (VLMs) struggle with Zero-Shot Anomaly Detection (ZSAD) due to a critical adaptation gap: they lack the local inductive biases required for dense prediction and employ inflexible feature fusion paradigms. We address these limitations through an Architectural Co-Design framework that jointly refines feature representation and cross-modal fusion. Our method proposes a parameter-efficient Convolutional Low-Rank Adaptation (Conv-LoRA) adapter to inject local inductive biases for fine-grained representation, and introduces a Dynamic Fusion Gateway (DFG) that leverages visual context to adaptively modulate text prompts, enabling a powerful bidirectional fusion. Extensive experiments on diverse industrial and medical benchmarks demonstrate superior accuracy and robustness, validating that this synergistic co-design is critical for robustly adapting foundation models to dense perception tasks. The source code is available at https://github.com/cockmake/ACD-CLIP.

cs.CV↗

arXiv2024

Facilitating Battery Swapping Services for Freight Trucks with Spatial-Temporal Demand Prediction

Electrifying heavy-duty trucks offers a substantial opportunity to curtail carbon emissions, advancing toward a carbon-neutral future. However, the inherent challenges of limited battery energy and the sheer weight of heavy-duty trucks lead to reduced mileage and prolonged charging durations. Consequently, battery-swapping services emerge as an attractive solution for these trucks. This paper employs a two-fold approach to investigate the potential and enhance the efficacy of such services. Firstly, spatial-temporal demand prediction models are adopted to predict the traffic patterns for the upcoming hours. Subsequently, the prediction guides an optimization module for efficient battery allocation and deployment. Analyzing the heavy-duty truck data on a highway network spanning over 2,500 miles, our model and analysis underscore the value of prediction/machine learning in facilitating future decision-makings. In particular, we find that the initial phase of implementing battery-swapping services favors mobile battery-swapping stations, but as the system matures, fixed-location stations are preferred.

eess.SY↗

arXiv2023

Numerical stability and tensor nuclear norm

We present a notion of bilinear stability, which is to numerical stability what bilinear complexity is to time complexity. In bilinear complexity, an algorithm for evaluating a bilinear operator $β: \mathbb{U} \times \mathbb{V} \to \mathbb{W}$ is a decomposition $β= φ_1 \otimes ψ_1 \otimes w_1 + \dots + φ_r \otimes ψ_r \otimes w_r $; the number of terms $r$ captures the speed of the algorithm; and its smallest possible value, i.e., the tensor rank of $β$, quantifies the speed of a fastest algorithm. Bilinear stability introduces norms to the mix: The growth factor of the algorithm $\lVert φ_1 \rVert_* \lVert ψ_1 \rVert_* \lVert w_1 \rVert + \dots + \lVert φ_r \rVert_* \lVert ψ_r \rVert_* \lVert w_r \rVert$ captures the accuracy of the algorithm; and its smallest possible value, i.e., the tensor nuclear norm of $β$, quantifies the accuracy of a stablest algorithm. To substantiate this notion, we establish a bound for the forward error in terms of the growth factor and present numerical evidence comparing various fast algorithms for matrix and complex multiplications, showing that larger growth factors correlate with less accurate results. Compared to similar studies of numerical stability, bilinear stability is more general, applying to any bilinear operators and not just matrix or complex multiplications; is more simplistic, bounding forward error in terms of a single (growth) factor; and is truly tensorial like bilinear complexity, invariant under any orthogonal change of coordinates. As an aside, we study a new algorithm for computing complex multiplication in terms of real, much like Gauss's, but is optimally fast and stable in that it attains both tensor rank and nuclear norm.

math.NA↗

arXiv2023

Complex matrix inversion via real matrix inversions

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^{-1}$ when $A$ is invertible, which may be traced back to Frobenius but has received scant attention. We prove that it is optimal, requiring fewest matrix multiplications and inversions over the base field, and we extend it in three ways: (i) to any invertible $A + iB$ without requiring $A$ or $B$ be invertible; (ii) to any iterated quadratic extension fields, with $\mathbb{C}$ over $\mathbb{R}$ a special case; (iii) to Hermitian positive definite matrices $A + iB$ by exploiting symmetric positive definiteness of $A$ and $A + BA^{-1}B$. We call all such algorithms Frobenius inversions, which we will see do not follow from Sherman--Morrison--Woodbury type identities and cannot be extended to Moore--Penrose pseudoinverse. We show that a complex matrix with well-conditioned real and imaginary parts can be arbitrarily ill-conditioned, a situation tailor-made for Frobenius inversion. We prove that Frobenius inversion for complex matrices is faster than standard inversion by LU decomposition and Frobenius inversion for Hermitian positive definite matrices is faster than standard inversion by Cholesky decomposition. We provide extensive numerical experiments, applying Frobenius inversion to solve linear systems, evaluate matrix sign function, solve Sylvester equation, and compute polar decomposition, showing that Frobenius inversion can be more efficient than LU/Cholesky decomposition with negligible loss in accuracy. A side result is a generalization of Gauss multiplication to iterated quadratic extensions, which we show is intimately related to the Karatsuba algorithm for fast integer multiplication and multidimensional fast Fourier transform.

math.NA↗

arXiv2023

Uniform Convergence with Square-Root Lipschitz Loss

We establish generic uniform convergence guarantees for Gaussian data in terms of the Rademacher complexity of the hypothesis class and the Lipschitz constant of the square root of the scalar loss function. We show how these guarantees substantially generalize previous results based on smoothness (Lipschitz constant of the derivative), and allow us to handle the broader class of square-root-Lipschitz losses, which includes also non-smooth loss functions appropriate for studying phase retrieval and ReLU regression, as well as rederive and better understand "optimistic rate" and interpolation learning guarantees.

stat.ML↗

arXiv2022

Rank-constrained Hyperbolic Programming

We extend rank-constrained optimization to general hyperbolic programs (HP) using the notion of matroid rank. For LP and SDP respectively, this reduces to sparsity-constrained LP and rank-constrained SDP that are already well-studied. But for QCQP and SOCP, we obtain new interesting optimization problems. For example, rank-constrained SOCP includes weighted Max-Cut and nonconvex QP as special cases, and dropping the rank constraints yield the standard SOCP-relaxations of these problems. We will show (i) how to do rank reduction for SOCP and QCQP, (ii) that rank-constrained SOCP and rank-constrained QCQP are NP-hard, and (iii) an improved result for rank-constrained SDP showing that if the number of constraints is $m$ and the rank constraint is less than $2^{1/2-ε} \sqrt{m}$ for some $ε>0$, then the problem is NP-hard. We will also study sparsity-constrained HP and extend results on LP sparsification to SOCP and QCQP. In particular, we show that there always exist (a) a solution to SOCP of cardinality at most twice the number of constraints and (b) a solution to QCQP of cardinality at most the sum of the number of linear constraints and the sum of the rank of the matrices in the quadratic constraints; and both (a) and (b) can be found efficiently.

math.OC↗

arXiv2022

Fair Representation Clustering with Several Protected Classes

We study the problem of fair $k$-median where each cluster is required to have a fair representation of individuals from different groups. In the fair representation $k$-median problem, we are given a set of points $X$ in a metric space. Each point $x\in X$ belongs to one of $\ell$ groups. Further, we are given fair representation parameters $α_j$ and $β_j$ for each group $j\in [\ell]$. We say that a $k$-clustering $C_1, \cdots, C_k$ fairly represents all groups if the number of points from group $j$ in cluster $C_i$ is between $α_j |C_i|$ and $β_j |C_i|$ for every $j\in[\ell]$ and $i\in [k]$. The goal is to find a set $\mathcal{C}$ of $k$ centers and an assignment $ϕ: X\rightarrow \mathcal{C}$ such that the clustering defined by $(\mathcal{C}, ϕ)$ fairly represents all groups and minimizes the $\ell_1$-objective $\sum_{x\in X} d(x, ϕ(x))$. We present an $O(\log k)$-approximation algorithm that runs in time $n^{O(\ell)}$. Note that the known algorithms for the problem either (i) violate the fairness constraints by an additive term or (ii) run in time that is exponential in both $k$ and $\ell$. We also consider an important special case of the problem where $α_j = β_j = \frac{f_j}{f}$ and $f_j, f \in \mathbb{N}$ for all $j\in [\ell]$. For this special case, we present an $O(\log k)$-approximation algorithm that runs in $(kf)^{O(\ell)}\log n + poly(n)$ time.

cs.DS↗

arXiv2020

Line Outage Identification Based on AC Power Flow and Synchronized Measurements

This paper proposes a method of identifying single line outages in power systems based on phasor measurement unit (PMU) measurements and ac power flow models. In addition to the main identification algorithm, a rejection filter is introduced so that the preliminary identified results can be further processed and categorized into three types: correctly identified, misidentified and inconclusive (including correct-filtered and misidentified-filtered). The methods are systematically tested using test systems of various sizes for various PMU placements, and the results show that the proposed identification algorithm has a high identification accuracy and the proposed rejection filter is able to reduce the misidentified rate without significantly increasing the number of inconclusive cases.

eess.SY↗

arXiv2020

Is Local SGD Better than Minibatch SGD?

We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minimax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least sometimes improves over minibatch SGD; (3) We show that indeed local SGD does not dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.

cs.LG↗

arXiv2019

Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loads

A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis. The distinct features of this group of dimensionless numbers are that it relates physical quantities of the impacted structure with essential basis of the Density, the Length and the Velocity, and thus it can represent the scaled influence of material property, geometry characteristic and velocity on the behavior of structures. The newly 15 proposed dimensionless numbers reflect three advantages. (1) The intuitively clear physical significance of these dimensionless numbers, such as the ratios of force intensity, force, moment of inertia to the corresponding dynamic quantities, the Johnson's damage number Dn and Zhao's response number Rn etc. are naturally included. (2) The property of direct matching the dimensionless expression of response equations of dynamic problems with these dimensionless numbers through simple equation analysis; (3) The ability of addressing non-scaling problems for different materials and strain-rate-sensitive as well as the VSG (initial impact Velocity-dynamic flow Stress-impact mass G) system. Four classical impact models are used to verify the direct matching property and the non-scaling addressing ability of the DLV system by equation analysis. The results show that the proposed dimensionless number system is simple, clear and efficient, and we suggest using it to represent the scaled behavior of structures under impact loads.

physics.class-ph↗

arXiv2014

A Multi-factor Adaptive Statistical Arbitrage Model

This paper examines the implementation of a statistical arbitrage trading strategy based on co-integration relationships where we discover candidate portfolios using multiple factors rather than just price data. The portfolio selection methodologies include K-means clustering, graphical lasso and a combination of the two. Our results show that clustering appears to yield better candidate portfolios on average than naively using graphical lasso over the entire equity pool. A hybrid approach of using the combination of graphical lasso and clustering yields better results still. We also examine the effects of an adaptive approach during the trading period, by re-computing potential portfolios once to account for change in relationships with passage of time. However, the adaptive approach does not produce better results than the one without re-learning. Our results managed to pass the test for the presence of statistical arbitrage test at a statistically significant level. Additionally we were able to validate our findings over a separate dataset for formation and trading periods.

q-fin.PM↗